f(x),g(x)的最小正周期分别为2π/k,π/k.
则2π/k+π/k=3π/2,得k=2.
则f(x)=Asin(2x+π/3),g(x)=Btan(2x-π/3）
因为f(π/2)=g(π/2),即Asin(π+π/3)=Btan(π-π/3),
A=2B ①
f(π/4)=-√3.g(π/4)+1,即Asin(π/2+π/3))=-√3.Btan(π/2-π/3)+1
A+2B=2 ②
联立①②,得
A=1,B=1/2
f(x)=sin(2x+π/3),g(x)=tan(2x-π/3)/2